the subject of the article is well adapted to a publication in cryosphere. The estimation of ice content from geophysical measurements is undoubtedly a very important purpose but complex and difficult subject to solve!
The complexity of the problem comes from the physic of the phase change but also from the methods used. The article is well written and the illustrations are good.
It is a pity that the authors did not validate the model with your synthetic cases or with laboratory measurements beforehand. the study site is interesting for the complexity in the distribution of permafrost.
thanks to the authors for this paper.
1) plan and purpose
the distribution of the parts is to be improved. the model used is too little developed whereas the instrumental part is too present.
The development of new instruments and measurement techniques in the field is a very interactive and an important subject but I advise to explain it another paper.
Indeed, the instrumental problems that are mentioned are numerous and are covered too quickly. Moreover, this is not really the subject of the article which is the estimation of ice content. if I am not mistaken.
The presentation of the results is a bit long, especially in relation with the geological context. This long presentation of the results is done at the expense of the discussion which is not sufficiently developed, especially on the chosen hypotheses and on the model.
2) Bibliography and freezing problem
the theoretical part is to be developed. It is focused on one type of approach without mentioning or discussing other models. Therefore, there is a lack of bibliographic references, especially on other approaches to model the SIP or HSIP response of an icy environment.
the focus of the model only on the polarization of the ice leads to a too simplistic model to model correctly the SIP response of an icy medium. at least, you have to justify much more the assumptions.
in the introduction of the article it is mentioned that it is necessary to develop a tool to follow the evolution of permafrost melting (or its renewal). a presentation of the thermal process is necessary to add. I am thinking in particular of the frost curve to be presented (e.g. Watanabe and Mizoguchi 2002). It is important to remember that permafrost consists of a solid fraction, a pore space filled with air, water and ice. Depending on the temperature and the initial water content of the soil, the ice content of a soil can be low. I'm not sure the assumption of just focusing on ice polarization is acceptable or shrewd. moreover, along an ERT profile, the lateral variations of lithology necessarily cause a variation in the importance of the polarizations of the medium and of the ice.
from the outset, the model used is intended to be high frequency in order to focus on the polarization of the ice. however, there is no mention of the physical processes explaining why there is high frequency ice polarization (Bjerrum effect, interface polarization...). by the way, what is the frequency range of this model? we are talking about high frequency (greater than 100khz) for the ice effect but also at much lower frequencies of the order of 100 Hz. In this case, for low frequencies, the broadband model must integrate the polarizations of Maxwell Wagner and of the electric double layer. otherwise, one must clearly justify why the polarization of the electric double layer is negligible.
the addition of a figure from synthetic data showing the impact of the variation of a parameter on the overall response will be appreciated. Finally, the development of a broadband model is very complex even for a soil without frost and requires validating this model from laboratory measurements. Validation of the model remains to be done. the site studied should rather be seen as an application of this model.
4) Instrumental part
the instrumental part is very interesting, but it could be reduced or make a paper in itself. Adding some advice, benchmarking on acquiring good measurements will be appreciated.
the presentation part of the site is well built as well as the result part. it would be appreciated to improve legend and caption of the figures in relation to the result (indicate the limits of different area, the active layer, the permafrost..). The result part could be condensed especially in the description of the different areas more or less frozen in order to add a few lines on the processing of the measurements (number of measurements acquired and filtered, frequencies used…) and on the inversion.
what is missing is a more relevant discussion, particularly on the model and the assumptions used.
L4-5: “The High-Frequency Induced Polarization method (HFIP) enables the measurement of the frequency dependent electrical signal of the subsurface”
Could you specify the frequency range?
The terms “electrical signal” it is not the most suitable. Maybe specify the name of the parameters that depend on frequency (conductivity and polarization) or the name of the processes (polarization and conduction processes).
L 6: “In contrast to the well-established Electrical Resistivity Tomography (ERT), the usage of the full spectral information provides additional physical parameters of the ground”
additional physical parameters: could you add some examples CEC, clay content, ice content...
L 11-14: “Amongst other improvements, compared to a previous generation, the new system is equipped with longer cables and larger power, such that we can now achieve larger penetration depths up to 10m.”
The paper is not about the development of a new measuring instrument but rather about a methodology to determine the ice content. Maybe reduce the paragraph on this new instrument and detail the methodology in the abstract.
L 5: “The frequency dependent electrical properties of ice have been studied by several authors over the past decades in the laboratory for pure ice as well as for ice within sediment mixtures (e.g. Auty and Cole, 1952; Hippel, 1988; Bittelli et al., 2004; Grimm et al., 2015; Artemov, 2019).
complete some references for example:
Coperey, A., A. Revil, et al. « Low‐Frequency Induced Polarization of Porous Media Undergoing Freezing: Preliminary Observations and Modeling ». Journal of Geophysical Research: Solid Earth, https://doi.org/10.1029/2018JB017015.
Olhoeft, G. R. (1977). Electrical properties of natural clay permafrost. Canadian Journal of Earth Sciences, 14(1), 16–24. https://doi.org/10.1139/e77‐002
L 19: “Attempts have been made to estimate ice content with one method only”
complete some references.
maybe you think about studies like Duvillard, 2018 « Three-Dimensional Electrical Conductivity and Induced Polarization Tomography of a Rock Glacier ». Journal of Geophysical Research: Solid Earth.
L 20: “A promising parameter is the frequency-dependent electrical permittivity.”
there is also the work of Petrenko, 1993; Petrenko and Ryzhkin, 1997, which is very interesting on the dielectric properties of ice.
L 6: “The previous studies were limited to qualitative interpretation with respect to ice content. “
Please add some references
L 6: Partly due to the lack of penetration depth of the acquisition system, […]
please, explain why?
I do not see why the lack of depth of investigation causes a quantitative interpretation of the ice content. Moreover, the depth of investigation in a resistant medium is not so bad compared to a conductive medium which requires more injection power and larger profile. Can you detail and give examples of study. thank you
L 19: “It contains the full information about the two material dependent properties of the ground: the electrical resistivity _ and the relative dielectric permittivity “
general remark not requiring change: it is better to speak or express electrical conductivity rather than electrical resistivity in the purely physical or petrophysical sense, i.e., electrical conductivity is really a material property (in the same way as thermal conductivity). Talking in electrical resistivity is right but less relevant from a physical point of view.
L 23: “Several reasons for polarizability are known, which can be distinguished by their strength and their occurrence in frequency range (Loewer et al., 2017).”
the terms “process” is more correct instead of reasons.
L 8: “In general, there is a choice whether the data interpretation is based on imaginary conductivity, or on the real part of permittivity, because the two are mathematically equivalent. Whereas for low-frequency (< 100Hz) SIP measurements, imaginary 10 conductivity is often preferred (Loewer et al., 2017), for high-frequency SIP covering the relaxation of ice, permittivity is generally considered (Bittelli et al., 2004).”
Yes, in fact for broad band SIP, this is better to consider the couple (conductivity and the permittivity). Each parameter is related to a specific process. You can find some extra information with Australian group papers like N. Wagner, T. Bore, A. Scheuermann…
L 26: “The inversion leads to the distribution of all five model parameters, […]”
What are these five parameters?
L 32: “and on physical models, such as the Maxwell-Wagner polarization, (e.g. Kozhevnikov and Antonov, 2012; Zorin and Ageev, 2017).”
What do you think of approaches that are based on the polarization of the electric double layer i.e. that do not take into account the polarization of the ice (in the strict sense) but its impact on the polarization of the double layer. (see for example coperey 2018, coperey 2021). A broad brand model based only on the polarization of the ice seems insufficient to me, especially if it wants to be broad band model.
L 5: “In that theory it is assumed, that the polarization is fully caused by the ice fraction.”
It depends on the frequencies you consider i.e. at 100 Hz you have the beginning of the polarization of the Maxwell Wagner and possibly the end of the polarization of the electric double layer for fine minerals like clay which are also very polarizable.
L10: “[…] the temperature dependence of the electrical parameters has been neglected.”
the variation of the resistivity is 2%/°C. it is not because you are close to the melting point that you can neglect this dependence i.e. which is also valid below the melting point. Indeed, the dependence is linked to the mobility of the ions and below the melting/freezing point, there is still some liquid water in the medium.
You can neglect this dependence if the system you are studying does not vary in temperature (or very little) or if you are studying at a given time.
L10: “Furthermore, other factors such as the clay content and, in general, low-frequency polarization effects were neglected, since the resulting effects in materials containing ice are much smaller than the polarization of ice.”
Please explain. This hypothesis must be really justified and clearly indicated in which case it is valid (e.g. low CEC or clay content, low salinity, frequency range used).
Precisely, neglecting the polarization of the EDL in some cases can lead to a wrong estimation.
L23: “Impedance measurements at the field scale with 4-point configurations up to 230kHz pose special challenges on the hardware.”
why this specific frequency?
Is the 4-point measurement still judicious to use at high frequency?
L9: “The phase shift is shown up to 115kHz, however, for the magnitude, values are only displayed until 60kHz, […]”
if from 60 kHz, the magnitude values have too much error then how can we be sure that the phase shift values are good?
moreover, for the models to be used it is necessary to have the magnitude/phase shift couple. What is then the interest to show the phase shift beyond 60 kHz ?
L18-19: “If we assume electrical parameters resistivity and permittivity as independent of frequency, […]”
why do you want to make these parameters independent of frequency, if this is the case why do measurements in the spectral domain?
L30:” The resistivity (panel a) is the same parameter as determined by other electric or electromagnetic methods in geophysics, for example by ERT, and can be compared with those results.”
not really, the different methods excite the medium in different ways (assumptions, frequencies, processes, volume of soil investigated are different). The profiles will therefore be different. What do you think about it?
L10: “The relaxation time for this layer is in the range of literature value for ice relaxation close to the melting point.”
Please add a value range and references.
L19-20: “The borehole information on frozen and unfrozen state, in combination with the soil moisture measurements (fig. 5) even allows a quantitative assessment of the estimated ice content. The soil moisture in the frozen sections of the borehole can be directly transferred to ice content.”
even when the soil is frozen, there is still a liquid fraction present in the soil. thus, the water content cannot be converted directly into ice content. it is necessary to know the freezing curve (see Watanabe 2005). especially when you are in the active zone
one could possibly admit a direct relation between water content and ice content under the eutectic of water (approximately -21°C) and still, there is the segregation of the salts present in water.
How do you explain the few percentage differences, especially on the amplitude for the reciprocal measurements? Why did you choose measurements from an alpine site and not from the Yakutia site?
what do the colours represent?
the high frequency adjustment is only controlled by the phase?
maybe you can change the colour of the high frequency fit curve for the |z| magnitude and explain its behaviour in the figure legend.
the text next to the peak is not very relevant (increasing/decreasing peak with depth), it is better to indicate the relationship between the ice content and the peak size
figure 8: Label the different sections in terms of zone (active zone, frozen zone).